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Spatial-temporal variation in environmental conditions is ubiquitous in nature. This variation simultaneously impacts survival, reproduction, and movement of individuals and thereby the rate at which metapopulations grow. Using the tools of stochastic demography, the metapopulation growth rate is decomposed into five components corresponding to temporal, spatial, and spatial-temporal variation in fitness and spatial and spatial-temporal covariation in dispersal and fitness. While temporal variation in fitness always reduces the metapopulation growth rate, all other sources of variation can either increase or reduce the metapopulation growth rate. Increases occur either by reducing the impacts of temporal variation or by generating a positive fitness-density covariance where individuals tend to concentrate in higher-quality patches. For example, positive autocorrelations in spatial-temporal variability in fitness generate this positive fitness-density covariance for less dispersive populations but decrease it for highly dispersive populations (e.g., migratory species). Negative autocorrelations in spatial-temporal variability have the opposite effects. Positive covariances between movement and future fitness, on short or long timescales, increase growth rates. These positive covariances can arise in unexpected ways. For example, the win-stay, lose-shift dispersal strategy in negatively autocorrelated environments can generate positive spatial covariances that exceed negative spatial-temporal covariances. This decomposition of the metapopulation growth rate provides a way to quantify the relative importance of fundamental sources of variation for metapopulation persistence. 

To understand infectious disease dynamics, we need to understand the inextricably intertwined nature of the ecology and evolution of pathogens and hosts. Epidemiological dynamics of many infectious diseases have highlighted the importance of considering the demographics of the societies in which they spread, particularly with respect to age structure. In addition, the waves of the recent COVID-19 pandemic driven by variant replacements at an unprecedented speed show that it is vital to consider the evolutionary aspects. The classic trade-off theory of virulence addresses aspects of pathogen evolution, but here we explore in more detail the possibility of society-specific evolutionarily stable strategies (ESS) during an unfolding pandemic. Theory posits the existence under some conditions of an ESS representing the evolutionary endpoint of change. By using a demographically realistic model incorporating infection rates that vary with age, we outline which evolutionary scenarios are plausible. Focusing on the rate of infection and duration of infectivity, we ask whether an ESS exists, what characterizes it, and as a result which long-term public-health consequences may be expected. We demonstrate that the ESS of an evolving pathogen depends upon the background age-dependent frailty and mortality rates. Our findings shed important light on the plausible long-term trajectories of highly evolvable novel pathogens. 

The relative arrival time of species can affect their interactions and thus determine which species persist in a community. Although this phenomenon, called priority effect, is widespread in natural communities, it is unclear how it depends on the length of growing season. Using a seasonal stage-structured model, we show that differences in stages of interacting species could generate priority effects by altering the strength of stabilizing and equalizing coexistence mechanisms, changing outcomes between exclusion, coexistence and positive frequency dependence. However, these priority effects are strongest in systems with just one or a few generations per season and diminish in systems where many overlapping generations per season dilute the importance of stage-specific interactions. Our model reveals a novel link between the number of generations in a season and the consequences of priority effects, suggesting that consequences of phenological shifts driven by climate change should depend on specific life histories of organisms. 

Abstract To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to an ergodic measure supporting other species. In the ecological literature, coexistence often is equated with the invasion growth rates being positive. Intuitively, positive invasion growth rates ensure that species recover from being rare. To provide a mathematically rigorous framework for this approach, we prove theorems that answer two questions: (i) When do the signs of the invasion growth rates determine coexistence? (ii) When signs are sufficient, which invasion growth rates need to be positive? We focus on deterministic models and equate coexistence with permanence, i.e., a global attractor bounded away from extinction. For models satisfying certain technical assumptions, we introduce invasion graphs where vertices correspond to proper subsets of species (communities) supporting an ergodic measure and directed edges correspond to potential transitions between communities due to invasions by missing species. These directed edges are determined by the signs of invasion growth rates. When the invasion graph is acyclic (i.e. there is no sequence of invasions starting and ending at the same community), we show that permanence is determined by the signs of the invasion growth rates. In this case, permanence is characterized by the invasibility of all$$-i$$ $-i$communities, i.e., communities without speciesiwhere all other missing species have negative invasion growth rates. To illustrate the applicability of the results, we show that dissipative Lotka-Volterra models generically satisfy our technical assumptions and computing their invasion graphs reduces to solving systems of linear equations. We also apply our results to models of competing species with pulsed resources or sharing a predator that exhibits switching behavior. Open problems for both deterministic and stochastic models are discussed. Our results highlight the importance of using concepts about community assembly to study coexistence. 

For species primarily regulated by a common predator, the P * rule of Holt & Lawton (Holt & Lawton, 1993. Am. Nat. 142 , 623–645. ( doi:10.1086/285561 )) predicts that the prey species that supports the highest mean predator density ( P *) excludes the other prey species. This prediction is re-examined in the presence of temporal fluctuations in the vital rates of the interacting species including predator attack rates. When the fluctuations in predator attack rates are temporally uncorrelated, the P * rule still holds even when the other vital rates are temporally auto-correlated. However, when temporal auto-correlations in attack rates are positive but not too strong, the prey species can coexist due to the emergence of a positive covariance between predator density and prey vulnerability. This coexistence mechanism is similar to the storage effect for species regulated by a common resource. Negative or strongly positive auto-correlations in attack rates generate a negative covariance between predator density and prey vulnerability and a stochastic priority effect can emerge: with non-zero probability either prey species is excluded. These results highlight how temporally auto-correlated species’ interaction rates impact the structure and dynamics of ecological communities. 

Many plant species worldwide are dispersed by scatter-hoarding granivores: animals that hide seeds in numerous, small caches for future consumption. Yet, the evolution of scatter-hoarding is difficult to explain because undefended caches are at high risk of pilferage. Previous models have attempted to solve this problem by giving cache owners large advantages in cache recovery, by kin selection, or by introducing reciprocal pilferage of ‘shared’ seed resources. However, the role of environmental variability has been so far overlooked in this context. One important form of such variability is masting, which is displayed by many plant species dispersed by scatterhoarders. We use a mathematical model to investigate the influence of masting on the evolution of scatter-hoarding. The model accounts for periodically varying annual seed fall, caching and pilfering behaviour, and the demography of scatterhoarders. The parameter values are based mostly on research on European beech ( Fagus sylvatica ) and yellow-necked mice ( Apodemus flavicollis ). Starvation of scatterhoarders between mast years decreases the population density that enters masting events, which leads to reduced seed pilferage. Satiation of scatterhoarders during mast events lowers the reproductive cost of caching (i.e. the cost of caching for the future rather than using seeds for current reproduction). These reductions promote the evolution of scatter-hoarding behaviour especially when interannual variation in seed fall and the period between masting events are large. This article is part of the theme issue ‘The ecology and evolution of synchronized seed production in plants’.